In contrast, the timing-based method spearheaded by SpikeProp [1]} provides a solution for computing exact gradients using spike timing. What is more, Mostafa [2]} explicitly derives spike timing gradients for non-leaky IF neuron models, leading to superior performance. Furthermore, Comsa et al. [3]} and Göltz et al. [4]} extended the method to LIF neuron models that also account for current leakage. The rate-based method backpropagates the gradient from the postsynaptic current to the presynaptic membrane potential regardless of the presence of spike firing events, whereas the timing-based method backpropagates the gradient between layers via the spike timing. Therefore, the timing-based method can avoid the problem of indifferentiability without the rate-based coding scheme. This point suggests the potential of the temporal-coding properties of timing-based methods. In general, timing-based methods adopt time-to-first-spike (TTFS) as a coding method, which converts the intensity of input information into absolute spike timing, and also they impose single-spike restrictions on all neurons [5]}, [3]}, [4]}, [8]}. These ideas are supported by the physiological studies [9]}, [10]} that argue that the first spike retains more information than the later ones. On the other hand, we define multi-spike SNNs as the networks in which individual neurons are allowed to fire multiple times, in contrast to SNNs with single-spike restrictions. It is clear that the single-spike restriction per neuron limits the learning efficiency and information processing capacity of SNNs. Furthermore, since biological neural networks are multi-spike, multi-spike is essential for investigating the coding properties of SNNs. Some researches tried on timing-based learning of multi-spike SNNs, but their results do not indicate that multi-spike SNNs were effective enough to outperform SNNs with single-spike restrictions [11]}, [12]}.
